Abstract
Many industrial optimization cases present themselves in a multi-objective (MO) setting (where each of the objectives portrays different aspects of the problem). Therefore, it is important for the decision-maker to have a solution set of options prior to selecting the best solution. In this work, the weighted sum scalarization approach is used in conjunction with three meta-heuristic algorithms; differential evolution (DE), chaotic differential evolution (CDE) and gravitational search algorithm (GSA). These methods are then used to generate the approximate Pareto frontier to the green sand mould system problem. The Hypervolume Indicator (HVI) is applied to gauge the capabilities of each algorithm in approximating the Pareto frontier. Some comparative studies were then carried out with the algorithms developed in this work and that from the previous work. Analysis on the performance as well as the quality of the solutions obtained by these algorithms is shown here.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Eschenauer, H., Koski, J., Osyczka, A.: Multicriteria Design Optimization. Springer, Berlin (1990)
Statnikov, R.B., Matusov, J.B.: Multicriteria Optimization and Engineering. Chapman and Hall, New York (1995)
Zitzler, E., Thiele, L.: Multiobjective optimization using evolutionary algorithms—A comparative case study. In: Eiben, A.E., Bäck, T., Schoenauer, M., Schwefel, H.-P. (eds.) PPSN 1998. LNCS, vol. 1498, pp. 292–301. Springer, Heidelberg (1998)
Deb, K., Pratap, A., Agarwal, S., Meyarivan, T.: A Fast and Elitist Multi-Objective Genetic Algorithm: NSGA-II. IEEE Transactions on Evolutionary Computation 6(2), 182–197 (2002)
Fishburn, P.C.: Additive Utilities with Incomplete Product Set: Applications to Priorities and Assignments. Operations Research Society of America (ORSA), Baltimore, MD, U.S.A (1967)
Triantaphyllou, E.: Multi-Criteria Decision Making: A Comparative Study, pp. 320–321. Kluwer Academic Publishers (now Springer), Dordrecht (2000)
Luyben, M.L., Floudas, C.A.: Analyzing the interaction of design and control. 1. A Multiobjective Framework and Application to Binary Distillation Synthesis, Computers and Chemical Engineering 18(10), 933–969 (1994)
Das, I., Dennis, J.E.: Normal-boundary intersection: A new method for generating the Pareto surface in nonlinear multicriteria optimization problems. SIAM Journal of Optimization 8(3), 631–657 (1998)
Eschenauer, H., Koski, J., Osyczka, A.: Multicriteria Design Optimization. Springer, Berlin (1990)
Sandgren, E.: Multicriteria design optimization by goal programming. In: Adeli, H. (ed.) Advances in Design Optimization, pp. 225–265. Chapman & Hall, London (1994)
Stanikov, R.B., Matusov, J.B.: Multicriteria Optimization and Engineering. Chapman and Hall, New York (1995)
Grosan, C.: Performance metrics for multiobjective optimization evolutionary algorithms. In: Proceedings of Conference on Applied and Industrial Mathematics (CAIM), Oradea (2003)
Zitzler, E., Thiele, L.: Multiobjective Optimization Using Evolutionary Algorithms - A Comparative Case Study. In: Eiben, A.E., Bäck, T., Schoenauer, M., Schwefel, H.-P. (eds.) PPSN 1998. LNCS, vol. 1498, pp. 292–301. Springer, Heidelberg (1998)
Knowles, J., Corne, D.: Properties of an Adaptive Archiving Algorithm for Storing Nondominated Vectors. IEEE Transactions on Evolutionary Computation 7(2), 100–116 (2003)
Igel, C., Hansen, N., Roth, S.: Covariance Matrix Adaptation for Multi-objective Optimization. Evolutionary Computation 15(1), 1–28 (2007)
Emmerich, M., Beume, N., Naujoks, B.: An EMO Algorithm Using the Hypervolume Measure as Selection Criterion. In: Coello Coello, C.A., Hernández Aguirre, A., Zitzler, E. (eds.) EMO 2005. LNCS, vol. 3410, pp. 62–76. Springer, Heidelberg (2005)
Fleischer, M.: The measure of Pareto optima. In: Fonseca, C.M., Fleming, P.J., Zitzler, E., Deb, K., Thiele, L. (eds.) EMO 2003. LNCS, vol. 2632, pp. 519–533. Springer, Heidelberg (2003)
Zitzler, E., Thiele, L., Laumanns, M., Fonseca, C.M., da Grunert Fonseca, V.: Performance Assessment of Multiobjective Optimizers: An Analysis and Review. IEEE Transactions on Evolutionary Computation 7(2), 117–132 (2003)
Surekha, B., Lalith, K.K., Panduy, A.K., Vundavilli, A.P.R., Parappagoudar, M.B.: Multi-objective optimization of green sand mould system using evolutionary algorithms. International Journal of Advance Manufacturing Technoloqy, 1–9 (2011)
Sushil, K., Satsangi, P.S., Prajapati, D.R.: Optimization of green sand casting process parameters of a foundry by using Taguchi method. International Journal of Advance Manufacturing Technology 55, 23–34 (2010)
Rosenberg, R.S.: Simulation of genetic populations with biochemical properties, Ph.D. thesis, University of Michigan (1967)
Storn, R., Price, K.V.: Differential evolution – a simple and efficient adaptive scheme for global optimization over continuous spaces, ICSI, Technical Report TR-95-012 (1995)
Rashedi, E., Nezamabadi-pour, H., Saryazdi, S.: GSA: A Gravitational Search Algorithm. Information Sciences 179, 2232–2248 (2009)
Zitzler, E., Thiele, L.: Multiobjective evolutionary algorithms: a comparative case study and the strength Pareto approach. IEEE Transactions on Evolutionary Computation 3(4), 257–271 (1999)
Kennedy, J., Eberhart, R.: Particle Swarm Optimization. In: IEEE Proceedings of the International Conference on Neural Networks, Perth, Australia, pp. 1942–1948 (1995)
Yang, X.S., Deb, S.: Cuckoo search via Lévy flights. In: Proc. of World Congress on Nature & Biologically Inspired Computing (NaBIC 2009), pp. 210–214. IEEE Publications, USA (2009)
Chatterjee, A., Mahanti, G.K.: Comparative Performance of Gravitational Search Algorithm and Modified Particle Swarm Optimization Algorithm for Synthesis of Thinned Scanned Concentric Ring Array Antenna. Progress in Electromagnetics Research B 25, 331–348 (2010)
Holland, J.H.: Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control and Artificial Intelligence. MIT Press, USA (1992)
Babu, B.V., Munawar, S.A.: Differential Evolution for the Optimal Design of Heat Exchangers. In: Proceedings of All-India seminar on Chemical Engineering Progress on Resource Development: A Vision 2010 and Beyond, Bhuvaneshwar (2000)
Babu, B.V., Singh, R.P.: Synthesis & Optimization of Heat Integrated Distillation Systems Using Differential Evolution. In: Proceedings of All- India seminar on Chemical Engineering Progress on Resource Development: A Vision 2010 and Beyond, Bhuvaneshwar (2000)
Angira, R., Babu, B.V.: Optimization of Non-Linear Chemical Processes Using Modified Differential Evolution (MDE). In: Proceedings of the 2nd Indian International Conference on Artificial Intelligence, Pune, India, pp. 911–923 (2005)
Colorni, A., Dorigo, M., Maniezzo, V.: Distributed Optimization by Ant Colonies. In: Proceedings of the First European Conference of Artificial Intelligence, pp. 134–142. Elsevier Publishing, Paris (1991)
Jakobson, M.: Absolutely continuous invariant measures for one-parameter families of one-dimensional maps. Communications on Mathematical Physics 81, 38–39 (1981)
Parappagoudar, M.B., Pratihar, D.K., Datta, G.L.: Non-linear modeling using central composite design to predict green sand mould properties. Proceedings IMechE B Journal of Engineering Manufacture 221, 881–894 (2007)
Shukla, P.K.: On the Normal Boundary Intersection Method for Generation of Efficient Front. In: Shi, Y., van Albada, G.D., Dongarra, J., Sloot, P.M.A. (eds.) ICCS 2007, Part I. LNCS, vol. 4487, pp. 310–317. Springer, Heidelberg (2007)
Zitzler, E., Knowles, J.D., Thiele, L.: Quality Assessment of Pareto Set Approximations. In: Branke, J., Deb, K., Miettinen, K., Słowiński, R. (eds.) Multiobjective Optimization. LNCS, vol. 5252, pp. 373–404. Springer, Heidelberg (2008)
Koza, J.R.: Genetic Programming: On the Programming of Computers by means of Natural Selection. MIT Press, USA (1992)
Zelinka, I.: Analytic programming by Means of SOMA Algorithm. In: Proc. 8th, International Conference on Soft Computing Mendel 2002, Brno, Czech Republic, pp. 93–101 (2002)
Ganesan, T., Vasant, P., Elamvazuthi, I.: Optimization of Nonlinear Geological Structure Mapping Using Hybrid Neuro-Genetic Techniques. Mathematical and Computer Modelling 54(11-12), 2913–2922 (2011)
Qu, B.Y., Suganthan, P.N.: Multi-objective evolutionary algorithms based on the summationof normalized objectives and diversified selection. Information Sciences 180, 3170–3181 (2010)
Li, K., Kwong, S., Cao, J., Li, M., Zheng, J., Shen, R.: Achieving Balance Between Proximity and Diversity in Multi-Objective Evolutionary Algorithm. Information Sciences 182, 220–242 (2011)
Elamvazuthi, I., Ganesan, T., Vasant, P.: A comparative study of HNN and Hybrid HNN-PSO techniques in the optimization of distributed generation (DG) power systems. International Conference on Advanced Computer Science and Information System (ICACSIS), 195–200 (2011)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Ganesan, T., Elamvazuthi, I., Shaari, K.Z.K., Vasant, P. (2013). Multiobjective Optimization of Green Sand Mould System Using Chaotic Differential Evolution. In: Gavrilova, M.L., Tan, C.J.K., Abraham, A. (eds) Transactions on Computational Science XXI. Lecture Notes in Computer Science, vol 8160. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-45318-2_6
Download citation
DOI: https://doi.org/10.1007/978-3-642-45318-2_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-45317-5
Online ISBN: 978-3-642-45318-2
eBook Packages: Computer ScienceComputer Science (R0)